Vague集的模糊熵、相似度量和距离测度的关系

Relations between Fuzzy Entropy,Similarity Measure and Distance Measure of Vague Sets

Vague集理论在各个领域中的广泛应用引起越来越多学者的注意,而模糊熵、相似度量和距离测度是其中的3个关键技术。目前已提出多种关于Vague集的模糊熵、相似度量和距离测度的计算方法,但这些研究都没有讨论这3个基本概念之间的联系。基于Vague集的模糊熵、相似度量和距离测度的公理化定义,给出了三者之间的相互诱导关系,建立了模糊熵、相似度量和距离测度之间的联系。

Vague sets theory has gained great attention from more and more researchers for its applications in various fields,fuzzy entropy,similarity measure and distance measure are the most important technologies in Vague sets.Nowadays,several formula about fuzzy entropy,similarity measure and distance measure of Vague sets have been proposed,but all of these researches did not discuss the relations between these measures.This paper based on the axiom definitions of fuzzy entropy,similarity measure and distance measure of Vague sets,gave mutual induced relations between these measures.Complete relations between fuzzy entropy,similarity measure and distance measure were established.